In a large skillet with high edges, heat 2 tablespoons of cooking fat over medium-high heat, swirling to coat the bottom of the pan. Season the chicken with salt and pepper and place in pan. Sear chicken until golden brown, about 3 minutes per side.

Remove the chicken from the pan and set aside. With the same pan still on medium-high heat, add the remaining 2 tablespoons cooking fat, onions, and peppers and sauté for 2 to 3 minutes, until the onion becomes translucent.

Add mushrooms and continue to cook, stirring for 2 minutes. Add garlic and stir until aromatic, about 1 minute, then add capers and diced tomatoes.

Return chicken to pan and cover everything with chicken broth or water. Reduce heat to medium and bring everything to a simmer.

Turn the heat down to low and continue to simmer (not boil) until the chicken reaches an internal temperature of 160°, about 30 minutes.

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